Create a cloth with two control points at each end? [video example included]
Maybe this file can point you the right way:



For simulation these kind of hairy strings, Soft Body Simulation is great. It's relatively fast to calculate, and it works on mesh edges by definition. In the sample scene, I just created an edge and subdivided it a few times. Then I added both end vertices to a group called Pinning, and created a hook for each end.

After that, I added a Soft Body Simulation to it, setting the Goal like this:



So very stiff, high damping, Goal Strength to 1 (so the end points will stick to the hooks), and choosing the Pinning Group to define the goal. When playing the animation, you get this: